Nonlinear Processes in Geophysics
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2010
10.5194/npg-17-319-2010
http://www.nonlin-processes-geophys.net/17/319/2010/
http://www.nonlin-processes-geophys.net/17/319/2010/npg-17-319-2010.html
http://www.nonlin-processes-geophys.net/17/319/2010/npg-17-319-2010.pdf
319
327
2010-07-19
Assessing microstructures of pyrrhotites in basalts by multifractal analysis
S. Xie
tinaxie2006@gmail.com
Q. Cheng
S. Zhang
K. Huang
State Key Laboratory of Geological Processes and Mineral Resources (GPMR), China University of Geosciences (CUG), Wuhan, 430074, China
Earth Science Faculty, China University of Geosciences (CUG), Wuhan, 430074, China
Department of Earth and Space Science and Engineering, York University, Toronto, ON, M3J 1P3, Canada
Institute of Resources and Environment, Shijiazhuang University of Economics, Hebei, 050031, China
Understanding and describing spatial arrangements of
mineral particles and determining the mineral distribution structure are
important to model the rock-forming process. Geometric properties of
individual mineral particles can be estimated from thin sections, and
different models have been proposed to quantify the spatial complexity of
mineral arrangement. The Gejiu tin-polymetallic ore-forming district,
located in Yunnan province, southwestern China, is chosen as the study area.
The aim of this paper is to apply fractal and multifractal analysis to
quantify distribution patterns of pyrrhotite particles from twenty-eight
binary images obtained from seven basalt segments and then to discern the
possible petrological formation environments of the basalts based on
concentrations of trace elements. The areas and perimeters of pyrrhotite
particles were measured for each image. Perimeter-area fractal analysis
shows that the perimeter and area of pyrrhotite particles follow a power-law
relationship, which implies the scale-invariance of the shapes of the
pyrrhotites. Furthermore, the spatial variation of the pyrrhotite particles
in space was characterized by multifractal analysis using the method of
moments. The results show that the average values of the area-perimeter
exponent (<i>D<sub>AP</sub></i>), the width of the multifractal spectra (Δ(<i>D(0)−D(2)</i>) and Δ(<i>D(q</i><sub>min</sub>)−<i>D(q</i><sub>max</sub>))) and the multifractality
index (τ"(1)) for the pyrrhotite particles reach their minimum in the second
basalt segment, which implies that the spatial arrangement of pyrrhotite
particles in Segment 2 is less heterogeneous. Geochemical trace element
analysis results distinguish the second basalt segment sample from other
basalt samples. In this aspect, the fractal and multifractal analysis may
provide new insights into the quantitative assessment of mineral
microstructures which may be closely associated with the petrogenesis as
shown by the bulk-rock geochemical analysis.
Agterberg, F. P., Cheng, Q., Brown, A., and Good, D.: Multifractal modeling of fractures in the Lac du Bonnet Batholith, Manitoba, Computers and Geosciences, 22(5), 497–507, 1996.
Bird, N., Diaz, C. M., Saa, A., and Tarquis, M.: Fractal and multifractal analysis of pore-scale images of soil, J. Hydrol., 322, 211–219, 2006.
Cheng, Q., Agterberg, F. P., and Ballantyne, S. B.: The separation of geochemical anomalies for background by fractal methods, Journal of Geochemical Exploration, 51, 109–130, 1994.
Cheng, Q.: The perimeter-Area Fractal Model and Its Application to Geology, Mathematical Geology, 27, 69–82, 1995.
Cheng, Q.: Multifractality and spatial statistics, Computers and Geosciences, 25(9), 949–961, 1999.
Cheng, Q.: Mapping singularities with stream sediment geochemical data for prediction of undiscovered mineral deposits in Gejiu, Yunnan Province, China, Ore Geology Reviews, 32(1–2), 314–324, 2007.
Evertsz, C. J. G. and Mandelbrot, B. B.: Multifractal measures (Appendix B) [A]. In: Peitgen H-O, Jurgens H, Saupe D, eds. Chaos and fractals[C]. New York: Springer Verlag, 922–953, 1992.
Flavio, S. A., Stefan, L., and Gregor, P. E.: Quantitative Characterization of Carbonate Pore Systems By Digital Image Analysis, AAPG Bulletin, 82(10), 1815–1836, 1998.
Gerard, R. E., Philipson, C. A., Manni, F. M., and Marshall, D. M.: Petrographic image analysis: and alternate method for determining petrophysical properties, in: Automated pattern analysis in petroleum exploration: New York, edited by: Palaz, I. and Sengupta, S. K., Springer Verlag, 249–263, 1992.
Hakon, W.: Volume, Shape, and Roundness of Rock Particles, J. Geol., 40(5), 443–451, 1932.
Halsey, T. C., Jensen, M. H., and Kadanoff, L. P.: Fractal measures and their singularities – the characterization of strange sets. Physical Review A 33(2), 1141–1151, 1986.
Krohn, C. E. and Thompson, A. H., Fractal sandstone pores: Automated measurements using scanning-electron-microscope images. Phys. Rev. B, 33, 6366–6374, 1986.
Li, Y., Qin, D., and Dang, Y.: Lithological Features of Basalt in Gejiu Eastern Area, Yunnan Province, Sci. Technol. Rev., 24(2), 70–72, 2006.
Li, Y., Qin, D., Dang, Y., Hong, T., and Yan, Y.: The distribution of the Indo-Chinese basalts in time and space in the eastern Gejiu, Journal of Chengdu university of Technology, 34(1), 23–28, 2007.
Liu, Y., Hu, Z., Gao, S., Günther, D., Xu, J., Gao, C., and Chen, H.: In situ analysis of major and trace elements of anhydrous minerals by LA-ICP-MS without applying an internal standard, Chemical Geology, 257, 34–43, 2008.
Lovejoy, S.: Area–perimeter relation for rain and cloud areas, Science, 216(4542):185–187, 1982.
Mandelbrot, B. B.: Fractals: form, chance, and dimension, Freeman, San Francisco, 1977.
Mandelbrot, B. B.: The fractal geometry of nature (updated and augmented edition), Freeman, New York, 1983.
McCauley, J. L.: Models of permeability and conductivity of porous media, Physica A, 187, 18–54,1992.
Meschede, M.: A method of discriminating between different types of mid-ocean ridge basalts and continental tholeiite with the Nb-Zr-Y diagram, Chemical Geology, 56, 207–218, 1986.
Muller, J. and McCauley, J. L.: Implication of fractal geometry for fluid flow properties of sedimentary rocks. Transp. Porous Media, 8, 133–147, 1992.
Muller, J., Huseby K. O., and Saucier A.: Influence of Multifractal scaling of pore geometry on permeabilities of sedimentary rocks. Chaos, Solitons and Fractals, 5(8), 1485–1492, 1995.
Muller, J.: Characterization of pore space in chalk by multifractal analysis, J. Hydrol., 187, 215–222, 1996.
Pachepsky, Y., Crawford, J. W., and Rawls W. J.: Fractals in soil science: Developments in Soil Science, Elsevier Science, Amsterdam, Hardbound, 2000.
Perrier, E., Bird, N., and Rieu, M.: Generalizing the fractal model of soil structure: the pore-solid fractal approach, Geoderma, 88(3–4), 137–164, 1999.
Sun, S. S. and McDonough, W. F.: Chemical and isotopic systematics of oceanic basalts: implications for mantle composition and processes, in: Magmatism in Ocean Basins, edited by: Saunders, A. D. and Norry, M. J., Geol. Soc. Spec. Publ., London, 313–345, 1989.
Tarquis, A. M., McInnes, K. J., Key, J. R., Saa, A., García, M. R., and Díaz, M. C.: Multiscaling analysis in a structured clay soil using 2D images, J. Hydrol., 322(1–4), 236–246, 2006.
Vidal Vázquez, E., Garc\'ia Moreno, R., Miranda, J. G. V., D\'iaz, M. C., Sa\' Requejo, A., Paz Ferreiro, J., and Tarquis, A. M.: Assessing soil surface roughness decay during simulated rainfall by multifractal analysis, Nonlin. Processes Geophys., 15, 457–468, doi:10.5194/npg-15-457-2008, 2008.
Wadell, H.: Volume, shape and roundness of rock particles, J. Geol., 40, 443–451, 1932.
Wang, Z., Cheng, Q., and Xia, Q.: The P-A fractal model characterizing microstructure of minerals, Proceedings of IAMG'05: GIS and Spatial Analysis, 317–322, 2005.
Wang, Z.: GIS-Based Fractal/multifractal modeling of texture in mylonites and banded sphalerite ores, Ph.D dissertation in the Department of Earth and Space Science and Engineering, York University, Canada, 2008.
Xie, S., Cheng, Q., Li, Z., Xing, X., and Chen, S.: Assessing Microstructures of Ore-minerals by multifractal, Earth Science – Journal of China University of Geosciences, 34(2), 263–269, 2009.
Xie, S., Cheng, Q., Ling, Q., Li, B., Bao, Z., and Fan, P.: Fractal and Multifractal Analysis of Carbonate Pore-scale Digital Images of Petroleum Reservoirs, Marine and Petroleum Geology, 27, 476–485, 2010a.
Xie, S., Cheng, Q., Xing, X., Bao, Z., and Chen, Z.: Geochemical multifractal distribution patterns in sediments from ordered streams, Geoderma, doi:10.1016/j.geoderma.2010.01.009, in press, 2010b.
Yu, C. W., Tang Y. J., and Shi P. F.: The Dynamic System of Polymetallic Metallogenic Province in Gejiu, Yunnan , Wuhan: Publishing House of China University of Geosciences, 394, 394 pp., 1988.
Zhang, Z., Mao, H., and Cheng, Q.: Fractal Geometry of Element Distribution on Mineral Surfaces, Mathematical Geology, 33(2), 217–228, 2001.
Zhijun Chen, Qiuming Cheng, Jiaoguo Chen, and Shuyun Xie: A novel iterative approach for mapping local singularities from geochemical data, Nonlin. Processes Geophys., 14, 317–324, doi:10.5194/npg-14-317-2007, 2007.
Zuo, R., Cheng, Q., Xia, Q., and Agterberg, F. P.: Application of Fractal Models to distinguish between different mineral phases, Mathematical Geosciences, 41, 71–80, 2009.